Abstract We study classifying problems for real hypersurfaces in a complex two-plane Grassmannian G2(ℂm+2). In relation to the generalized Tanaka–Webster connection, we consider a new concept of parallel normal Jacobi operator for real hypersurfaces in G2(ℂm+2) and prove that a real hypersurface in G2(ℂm+2) with generalized Tanaka–Webster 𝔇⊥-parallel normal Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍPn in G2(ℂm+2), where m = 2n.

中文翻译：

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具有广义Tanaka-Webster连接的复杂双平面Grassmannians中Hopf超曲面的𝔇⊥平行法线雅可比算子

摘要 我们研究了复杂的两平面格拉斯曼 G2(ℂm+2) 中真实超曲面的分类问题。关于广义的 Tanaka-Webster 连接，我们考虑了 G2(ℂm+2) 中真实超曲面的平行法线雅可比算子的新概念，并证明 G2(ℂm+2) 中的真实超曲面具有广义 Tanaka-Webster 𝔇⊥ -parallel normal Jacobi 算子在 G2(ℂm+2) 中与围绕完全测地四元数射影空间 ℍPn 的管的开放部分局部一致，其中 m = 2n。